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This study analyzes many-particle diffusion in one dimension, revealing universal power laws for extreme movement statistics. Measuring these extremes can uncover hidden environmental properties influencing particle motion.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • Many-particle diffusion is often modeled as random walks in a random environment.
  • Understanding the influence of the environment on particle motion is crucial.

Purpose of the Study:

  • To determine universal power laws for the environment's contribution to extreme statistics in many-particle diffusion.
  • To relate these universal behaviors to measurable properties of the random environment.

Main Methods:

  • Theoretical analysis of many-particle diffusion in one spatial dimension.
  • Modeling the system as random walks in a shared random environment.
  • Numerical verification across various models and system sizes.

Main Results:

  • Universal power laws were derived for the variance of extreme first passage time and extreme location.
  • Prefactors of these power laws depend on an extreme diffusion coefficient, linked to the environment's local drift variance.
  • This contrasts with the Einstein diffusion coefficient, which relates to jump variance in an averaged environment.

Conclusions:

  • Measuring extreme behaviors in many-particle diffusion provides a method to characterize hidden environmental fluctuations.
  • The findings offer insights into the statistical properties of random environments influencing diffusion.